Real-time location systems (so-called RTLS) allow the geographical position of a given target to be estimated, like for example a person or an object, in a given indoor or outdoor environment. Typically, RTLS systems are integrated in so-called Wireless Sensor Networks (WSN), consisting of wireless devices—all the nodes of the network—some of which are equipped with sensors, whose data is sent to other user nodes.
WSNs are special networks that may be created ad-hoc, i.e., with maximum flexibility, and they may be easily installed, removed, and updated thanks to the lack of cables. This makes them very versatile and not so invasive: indeed, they may be able to co-exist with any other network, and interact with or extend existing networks. Their topology is dynamic; it is typically not necessary to know a priori the deployments of the nodes, and the network maintains its connectivity, even if the nodes move or have failures in some of them.
One of the purposes of a network of sensors is to produce, over an extended time period, a single global information based on a series of local data coming from the single sensors.
The sensor nodes are equipped with an on-board micro-controller, although of limited capacity. This may allow communication to be minimized and thus allows energy usage to be optimized, since every node may have a limited power resource. Once set in operation, the node typically works autonomously; it may receive commands from the coordinator node that manages the network and execute them only if its embedded code implements the functions specified by the command. The design of a WSN uses the available information efficiently and effectively to define the resources, the coverage area, the organization of the nodes, and the level of cooperation among them.
There are multiple application scenarios for WSNs. Indeed, such networks may be seen as a set of sensors of different types capable of detecting magnitudes such as temperature, humidity, pressure, and light, but also capable of detecting the movement of vehicles, the composition of the land, the noise level, and many other quantities and characteristics. The application fields where the networks of sensors may have natural use are various: from commercial and industrial sectors to environmental sectors as well as at home.
In all these scenarios, location is one of the most relevant functionalities. Indeed, the interest in location derives from the fact that information measured by a device is of some interest only if it is space-time correlated, i.e., if we are aware of the time and place in which this quantity was measured. For example, the management of lighting in the various rooms of a building allows the various areas to be lit in a differentiated manner, even according to the external lighting or else whether or not somebody is at a specific desk. Therefore, a node or the network must know the node's position and in which room it was placed for the node and network to operate correctly.
Generally, for location methods, it is presumed that the positions of some nodes of the network are known and that these nodes will not move over time. These nodes are called “anchor nodes,” they are installed within the environment to be monitored, and, through an appropriate procedure of configuration, they “know” their own coordinates.
The other nodes, called “blind nodes,” do not know their own coordinates and may move within the environment to be monitored: for example they may be placed on mobile objects or they may be moved due to external events (e.g., wind or movement in water).
Main-location solutions proposed in the literature may be distinguished between centralized solutions and distributed solutions.
In the case of a centralized approach, there is a special node, the coordinator or a PC coupled to the network, which generally has greater calculation capacity and energy access with respect to the other nodes. Such a device collects the information coming from all the nodes of the network to determine their relative positions; then such information may be sent to the nodes that request it.
In the distributed approach, on the other hand, every node exchanges information just with the nodes close to it and each of the blind nodes uses the information available locally to determine its own position. An advantage of a distributed approach is the greater scalability; however, the computing capabilities of the nodes of a WSN are quite limited, and this entails restrictions on the complexity of the location algorithm in terms of clock cycles, information exchanged, and memory occupation.
A centralized system, on the other hand, suffers less from such limitations and may be easily implemented if there is already a functionality for a centralized collection of information. On the other hand, an algorithm of this type may require that every node belonging to the network sends messages to the calculation center, thus possibly creating an overload of communication that could risk clogging up the network. Moreover, such an approach may not be usable in environments with many nodes in motion, because of the delay of propagation and, finally, it may create problems relative to privacy.
In both approaches, the position of the blind nodes is generally determined by exploiting the information relative to the position of the anchor nodes in the monitored environment and the information that places the position of the blind nodes in relation with the position of the anchor nodes. Usually, for this functionality scope, the measurements of the distance deriving from the exploitation of the radio communications of the nodes and, therefore, of the radiofrequency signals properties, are used.
In general, location is performed in three steps: configuration, ranging, and estimation of the position.
In the configuration step, the positions of the anchor nodes placed into the environment that is to be monitored are fixed and the system is made aware of the information relative to these positions.
In the ranging step, the distances between each blind node and the various anchors are estimated.
In the step of estimating the position, the coordinates of the blind nodes within the environment that is to be monitored are estimated on the basis of the information obtained in the configuration step and in the ranging step. For example, the coordinates of the blind nodes may be estimated by lateration.
The ranging step, i.e., the step of estimating the distances, often represents the most critical step of the location process due to the various factors that may influence the measurements.
In the literature, there are many techniques for estimating the distances for wireless devices. In particular, various employed metrics are obtained from the signals exchanged between the nodes. For example, it is possible to use the Time of Fly (ToF), the Time difference of Arrival (TdoA), or the Angle of Arrival (AoA).
However, one of the metrics often used in literature for the ranging step is the so-called RSSI (Received Signal Strength Indicator), i.e., the energy level detected by the radio over the current channel and relative to the packet that is being received. Hypothesising a propagation model of the signal in air as a function of the distance, it may be possible to estimate the transmitter-receiver distance from the evaluation of the RSSI.
In particular, in the case of WSNs, the RSSI value may be measured directly from the radiofrequency signal used by the nodes to communicate data and control information. In this way, every device may obtain information on the distances from its nearby nodes by exploiting the normal reception of the packets, not requiring any additional hardware component. However, if on the one hand a location system based on the measurement of the RSSI values has the advantage of being cost-effective, on the other hand, a possible drawback is correlated to the highly dynamic nature of the received signal. The RSSI value, and consequently the distance estimation value, is greatly influenced by various phenomena which take place particularly in indoor environments. In particular, factors that influence the RSSI values indoors include the variability of the transmitter, the variability of the receiver, the orientation of the antenna, and the multi-path fading and shadowing of an RF channel.
In general, three main components are identified in the channel model that correlate the power received to the distance between the transmitter and the receiver: a dominant term that depends one the distance, a term that takes into account the slow fading, and a term that takes into account the fast fading.
The dominant term indicates that the received power has, as a function of the distance, a trend of the type:
                                          P            R                    ⁡                      (            d            )                          =                                            P              R                        ⁡                          (                              d                0                            )                                ⁢                                    (                                                d                  0                                d                            )                        a                                              (        1        )            
in which: PR(d0) represents the power (in Watts) received at the reference distance d0 (in meters) and the coefficient α is named as attenuation factor. The slow fading, which manifests itself with a series of slow oscillations of the power received with respect to the main component, is modelled by means of a Log-Normal distribution, whereas the fast fading, characterized by rapid oscillations around the slow fading component, is described through a Rice distribution.
Since the effects of the fast fading may be reduced through the use of Direct Sequence Spread Spectrum (DSSS) techniques, like those adopted for example in standard PHY IEEE 802.15.4, the model used to correlate the power received to the distance between the transmitter and the receiver may take into account just only the first two components. Therefore:
                                          P            R                    ⁡                      (            d            )                          =                                                            P                R                            ⁡                              (                                  d                  0                                )                                      ⁢                                          (                                                      d                    0                                    d                                )                            a                                +                      X            L                                              (        2        )            
in which χL represents a Log-Normal random variable.
Expressing the value of the power received in dBm, the equation (2) becomes:
                                                        P              R                        ⁡                          (              d              )                                            [            dBm            ]                          =                                                            P                R                            ⁡                              (                                  d                  0                                )                                                    [              dBm              ]                                +                      10            ⁢            α            ⁢                                                  ⁢                                          log                10                            ⁡                              (                                                      d                    0                                    d                                )                                              +                      X            g                                              (        3        )            where χg is a zero-mean Gaussian random variable with standard deviation σ.
From the previous equation follows the formula of the Path Loss Model:
                              PL          ⁡                      (            d            )                          =                              PL            0                    +                      10            ⁢            α            ⁢                                                  ⁢                                          log                10                            ⁡                              (                                  d                                      d                    0                                                  )                                              +                      X            g                                              (        4        )            in which:
PL(d)=PT−PR(d) represents the attenuation undergone by the radio signal transmitted at power PT after having traveled a distance equal to d;
PL0=PL(d0) is the attenuation measured at the reference distance d0.
The path-loss propagation model thus depends on different parameters like the attenuation coefficient, the power received, and the distances between the nodes.
The equation (4) may be expressed in dBm in order to refer directly to the RSSI values. The equation (4) thus becomes:
                    RSSI        =                              P            T                    -                      PL            ⁡                          (                              d                0                            )                                -                      10            ⁢            α            ⁢                                                  ⁢                                          log                10                            ⁡                              (                                  d                                      d                    0                                                  )                                              +                      X            g                                              (        5        )            
Given that χg is a Gaussian random variable that has an unknown power with zero mean, it may be possible to eliminate this term from the equation considering the statistical average of the magnitudes. Given that the process is ergodic since it is stationary, the statistical average converges to the temporal average. For these reasons, we thus consider the mean value of the RSSI received by every device.
The model obtained is thus:
                              RSSI          _                =                              P            0                    -                      10            ⁢            α            ⁢                                                  ⁢                                          log                10                            ⁡                              (                                  d                                      d                    0                                                  )                                                                        (        6        )            where RSSI is the mean value of the RSSI measured for the received packets coming from the same source.
The equation (6) shows that the power decay of a signal from the transmitter node to the receiver node depends on three parameters:                the reference distance d0;        the attenuation coefficient α that depends on the type of channel in which the signal propagates;        the value (P0) of the power received at the reference distance d0 (P0=PT−PL(d0)).        
In conventional RTLS systems based on RSSI, the parameters of the propagation model of the signal in air as a function of the distance are set a priori. In particular, for example, based on Patwari et al. “Relative Location Estimation in Wireless Sensor Networks”, IEEE Transactions on Signal Processing, August 2003, and R. Grossmann et al., “Localization in ZigBee-based Sensor Networks”, in IEEE International Symposium on Intelligent Signal Processing WISP 2007, the user is required to place any two nodes at a distance of 1 meter (d0) and to measure the RSSI value between this pair of nodes, before the installation of the location system. This value is used to set the P0 value, whereas α is selected among a series of probable values without however considering the environment and its distinctive features. Having done this, during the estimating of the blind-node positions, these values (d0, α, P0) are used to determine the unknown distances between the receivers and the transmitters in the following ranging steps.
However, using the same fixed values for the propagation model parameters during the entire time of measurement entails the introduction of substantial uncertainties in the obtained results. Indeed, due to what has been described above, it may be possible to measure variations in the RSSI values even in the case of fixed nodes, i.e., in the case in which the distances between the transmitters and receivers do not vary. Nevertheless, it may be possible to measure the same RSSI values even if the distances between the nodes are effectively modified.
The “a priori” statistic estimation of the channel model parameters may entail the introduction of substantial errors in the accuracy of the blind-node positions estimations since, due to what has been described above, the RSSI values may vary over time for various factors. In particular, the position-estimation errors may be substantially higher if long time windows are considered for carrying out the measurements.
Conventionally, in order to avoid the timing variability of the RSSI values, they are filtered, for example, discarding the anomalous values such as the spikes, or by applying statistical techniques based on the average calculation.
However, these provisions may be unable to ensure acceptable and stable accuracy levels. In particular, for example, in the case of environments influenced by substantial and various noise sources, conventional location systems may be unable to determine adequate and stable estimations of the positions of the nodes, since the values used for the channel-model parameters remain fixed over time.